. What does the epipolar constraint x2^T F x1 = 0 tell you about where a point's match must lie in the second image?
Given x1, the line l2 = F x1 is the epipolar line in image 2 that the true match is guaranteed to lie on, collapsing the search from 2D to 1D.
. Geometrically, why does a point's match always fall on a single line rather than anywhere in the second image?
All points along the ray from C1 through x1 share the same epipolar plane with C1 and C2; camera 2 sees that plane edge-on, so every candidate projects onto the same line.
. Why does the 8-point algorithm normalize pixel coordinates (centering and rescaling) before solving for F via SVD?
This is the Hartley normalization step: solving in centered, rescaled coordinates avoids numerical ill-conditioning that raw large pixel values would cause.
. Why can cv2.recoverPose only recover the *direction* of the translation between the two cameras, not its magnitude?
The scale ambiguity is fundamental to monocular two-view geometry: uniformly scaling the scene and baseline together produces identical images, so absolute scale can't be recovered from correspondences alone.